Dynamic Reconfiguration of Photovoltaic Energy Harvesting System in Hybrid Electric Vehicles

Yanzhi Wang1, Xue Lin1, Naehyuck Chang2, and Massoud Pedram1 1Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA

2Seoul National University, Seoul, Korea 1{yanzhiwa, xuelin, pedram}@usc.edu, 2{naehyuck}@elpl.snu.ac.kr

ABSTRACT

Photovoltaic (PV) energy harvesting system is a promising energy

source for battery replenishment in hybrid electric vehicles

(HEVs.) The PV cell array is installed on different parts of a

vehicle body such as the engine hood, door panels, and the roof

panel. Non-uniformity of the solar irradiance and temperature on

the PV cell array is, however, a serious obstacle to efficient

utilization of the PV system in HEVs because such variation, if

not managed properly, can result in a significant degradation in

the overall output power level of the PV system. This paper

presents a dynamic PV array reconfiguration technique with

structural support and a dynamic programming-based algorithm

with polynomial time complexity to produce the near-optimal

reconfiguration of the PV array on the HEV. The goal of this

technique is to maximize the PV system output power under any

solar irradiance and temperature distribution on the PV array. We

demonstrate up to 6X improvement in the output power of a PV

system against a conventional fixed configuration PV system.

Categories and Subject Descriptors

B.8.2 [Performance and Reliability]: Performance Analysis and Design Aids.

General Terms

Algorithms, Design, Management, Performance.

Keywords

Photovoltaic System, Hybrid Electric Vehicle, Photovoltaic Array Reconfiguration, Dynamic Programming.

1. INTRODUCTION With growing public consciousness about the greenhouse gas emissions and increase in the price of petroleum, hybrid electric vehicles (HEVs) are perceived as a core segment of future automotive market. HEVs employ both electric motors and internal combustion engines to improve the fuel economy. Batteries powering the electric motor in a HEV must be recharged by a generator in the HEV. On top of a regenerative braking-based battery charging scheme, a photovoltaic (PV) system mounted on the HEV can enable battery charging whenever there is solar irradiance. PV cells can be mounted on the roof panel, engine hood, trunk, and door panels of a HEV.

PV systems have been widely deployed for many applications since solar energy is abundant, renewable, and clean. A PV

system consists of a PV array and peripheral charging regulation circuitry (e.g., the charger). A PV array itself comprises multiple PV cells connected in a series-parallel configuration. Ideally, all PV cells in the array experience identical operational conditions and exhibit the same voltage-current (V-I) and voltage-power (V-P) output characteristics. Thus, they can simultaneously operate at their maximum power points (MPPs.) We can achieve the maximum output power of the PV array with a MPP tracking (MPPT) method [1][2]. Furthermore, the recently proposed maximum power transfer tracking (MPTT) technique can guarantee the maximum output power of the PV system under non-ideal behaviors of the charger [3]. In reality, PV cells may receive different solar irradiances due to partial shading and variations in the solar irradiance incidence angle. In addition, PV cells may experience different temperatures. For instance, PV cells on the door panel have a different solar irradiance incidence angle from those on the roof. PV cells on top of the hood have a higher temperature than PV cells on the roof.

Figure 1. V-I and V-P characteristics of a PV cell under

different solar irradiances.

Figure 2. V-I and V-P characteristics of a PV cell under

different temperatures.

Figures 1 and 2, where MPPs of a PV cell are marked by red dots, illustrate that a higher solar irradiance or a lower temperature lead to a higher output power at the MPP of the cell. Partial shading not only reduces the maximum output power of the shaded PV cell, but also makes non-shaded PV cells that are connected in series with the shaded one deviate from their MPPs.

0 1 2 30

0.5

1

1.5

2

Voltage (V)

Cu

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(A)

0 1 2 30

0.5

1

1.5

2

2.5

3

3.5

Voltage (V)

Po

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25 CG = 1.0

G = 0.8

G = 0.6

G = 0.4

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0 1 2 30

0.5

1

1.5

2

Voltage (V)

Curr

ent

(A)

0 1 2 30

0.5

1

1.5

2

2.5

3

3.5

Voltage (V)

Pow

er

(W)

25 C

40 C55 C

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109

Similarly, a hotter PV cell makes PV cells that are connected in parallel with it deviate from their MPPs. Thus PV cells in a PV array with solar irradiance and/or temperature non-uniformity cannot operate at their MPPs simultaneously, and thus, the PV array suffers from significant power inefficiency. In addition, the V-P characteristic curve of such a PV array shows multiple peaks. Therefore, the existing MPPT or MPTT techniques, which are based on the unimodality assumption of V-P characteristics, have to be modified to find the global optimal operating point of the PV array [4][5]. This fact increases the complexity of the PV system controller. Some PV array reconfiguration techniques have been proposed [6][7][8] to solve the PV system power loss problem due to solar irradiance and temperature non-uniformity phenomenon. These techniques suffer from the following shortcomings: i) they require extra PV cells to perform reconfiguration; ii) a systematic and scalable reconfiguration control mechanism is lacking; and iii) they do not consider charger efficiency variation in the PV system.

In this paper, we present a dynamic PV array reconfiguration technique, which updates the PV array configuration according to the change of irradiance and temperature distribution on the PV array during system operation in order to enhance the output power of PV systems. Our reconfiguration technique has the ability to simultaneously meet (to the extent that is possible) the MPPs for all PV cells even under non-uniform solar irradiance and temperature distributions. We provide both a scalable structural support and an effective control algorithm. The control algorithm realizes near-optimal PV array reconfiguration accounting for solar irradiance and temperature distributions and charger efficiency variation. The algorithm is based on dynamic programming with polynomial time complexity so that it can be integrated into PV systems with insignificant computational overhead. Experimental results demonstrate that our proposed dynamic reconfiguration technique results in up to 6X improvement in PV system output power compared with a conventional fixed array structure PV system.

2. PV SYSTEM MODEL AND RECONFIGURATION

Figure 3. System diagram of a PV-powered HEV.

Figure 3 shows the system diagram of a PV-powered HEV. The PV array consists of a number of PV cells, mounted on the roof panel, engine hood, trunk, and door panels of the HEV. Conventional HEVs are equipped with battery packs as the energy storage system, connected to the traction motor via the generator charger. The PV-powered HEV also has an add-on PV system that consists of a PV array and a PV charger connecting the PV array to battery packs. The generator charger and PV charger can simultaneously charge battery packs. MPPT or MPTT techniques are integrated with the PV charger, and therefore, the PV charger

can set the optimal operating point for the PV array. The PV array consists of a number of series-connected PV cell groups where each PV group consists of (potentially a different number of) PV cells connected in parallel. Although mounting positions of PV cells are fixed on the HEV, PV array reconfiguration technique adaptively changes the electric connection of PV cells in response to changes in the environmental condition. Figure 4 provides the equivalent circuit of the PV system shown in Figure 3, where the battery bank in Figure 4 represents the battery packs on HEV.

PV

Charger

Battery

Vbat

Ibat_pv

Pconv

Vpv

Ipv

PV Cell Array

Group #1

Group #2

Group #3

Generator

Charger

Ibat_motor

From Motor

Figure 4. Equivalent circuit of a PV system on a HEV.

2.1 Component Models It is necessary to have accurate component models, including models for the PV cell, battery and charger, in order to develop an effective PV array reconfiguration algorithm. Given the solar irradiance and temperature of a PV cell, the PV cell voltage

and current

satisfy certain V-I characteristics as shown in

Figures 1 and 2. The MPP (maximum power point) that

maximizes the PV cell output power

lies on the V-I curve.

In terms of the notation, we have:

at the MPP. We obtain the V-I characteristics and MPP of a PV

cell under any using the PV cell model of reference [10]. We adopt the battery and charger models from [11]. Generally speaking, the power conversion efficiency of a charger is a function of its input and output voltages and currents. The conversion efficiency is maximized when the charger output current is within a small operation range, and its input and output voltages are close to each other.

2.2 Reconfiguration Structure for PV Array A conventional PV array consists of n series-connected PV groups, whereby each PV group has exactly m parallel-connected PV cells, (all PV groups have the same number of PV cells.) In contrast, the PV array in Figure 4 has three series-connected PV cell groups, and there are different numbers of parallel-connected PV cells within the groups, which is an imbalanced configuration. Reference [9] presented a structural support mechanism for balanced reconfiguration of supercapacitor banks. In this paper, we exploit the structural support in [9] for the PV array. However, we allow more flexible configurations (both balanced and imbalanced) of PV cells in the PV array.

SpT,i

SpB,i

Ss,i

i-th

(a) (b)

1 i N

SpT,1

SpB,1

Ss,1

SpT,i

SpB,i

Ss,i

P-switch

P-switch

S-switch

Switch-Set

S-switch open

P-switches closed

S-switch closed

P-switches open

Figure 5. Reconfiguration structure.

We demonstrate the possibility of creating an imbalanced reconfiguration using the reconfiguration structure of [9]. The PV cells are integrated with a series switch and a pair of parallel

switches and , as shown in Figure 5 (a). The PV array has

a reconfiguration structure as shown in Figure 5 (b), where the PV array consists of N PV cells and all the PV cells except for the last one are integrated with switches. We can realize PV array

110

reconfiguration by controlling the states of switches. For any PV cell, its two parallel switches are always in the same state, so we

use to denote the pair of parallel switches in i-th PV cell of

the array. is used for connecting the PV cells in parallel, and

is used for connecting the PV cell groups in series. If is on,

must be off; if is on then must be off. Figure 6 shows

the states of switches to realize the imbalanced configuration

shown in Figure 4, where group #1 is formed by turning on

through to form a group of five parallel connected PV cells

whereas groups #1 through #3 are series-connected by turning on

and .

Sp,1

1 2 3 4 5

8

Sp,6

6

Sp,7

7

Sp,2 Sp,3 Sp,4

9 10 11 12

Sp,9 Sp,10 Sp,11

Ss,5

Ss,8

Group #1

Group #2

Group #3

Figure 6. Example of imbalanced configuration.

In the PV array configurations achieved by the reconfiguration structure, the number of groups n in the PV array can be any positive integer less than or equal to N. The number of parallel-

connected PV cells in each group should satisfy

= N. (1)

We denote such a configuration as , which could be viewed as a partition of the PV cell index set =

, where integers in denote the indices of the PV

cells in the PV array. The partition is denoted by n subsets , , , and , which correspond to the n groups consisting of ,

, , and PV cells, respectively. The subsets , , , and satisfy

, (2)

and

, for and . (3)

Furthermore, the integer values in subset must be smaller than

the integer values in subset , for any , due to the structural characteristics of the proposed reconfiguration technique. A partitioning satisfying the above properties is called an alphabetical partitioning.

3. PROBLEM FORMULATION 3.1 Problem Statement The solar irradiance distribution over the PV array on the HEV changes over time, due to driving direction change and shading caused by buildings, clouds, and other moving vehicles. Temperature variation is also severe because of the engine heat dissipation and convection due to airflow. We should perform the

PV array reconfiguration algorithm at every decision epoch to maximize the PV system output power. For notational

convenience, we drop the time index . We denote the solar irradiance and PV cell temperature of the i-th ( ) PV cell

by and , respectively. We obtain and values using irradiance and temperature sensors in the system. We denote the

output voltage and current of the i-th PV cell by and

,

respectively. The PV array configuration is the major control variable of the reconfiguration algorithm.

We develop V-I characteristic of the PV array with a

configuration that corresponds to the alphabetical partitioning , , , and as follows. We use

to denote the output voltage of the j-th PV group, and use

and to denote the output voltage and current of the PV

array, respectively. The and values can be effectively

controlled by the PV charger. From the Kirchhoff’s laws, we have:

(4)

, for and (5)

and

(6)

We control and maintain the PV array operating point using the PV charger. The power loss of the PV charger, , is calculated from its input voltage, input current, output voltage,

and output current, i.e., , , , and , respectively

[11]. Due to the energy conservation law, we have:

(7)

where and are the battery’s terminal voltage and

charging current from the PV system, respectively. The formal problem statement of the PV array reconfiguration (PAR) problem for HEV is described as follows:

PAR Problem Statement: Given the solar irradiance and the

temperature of each i-th ( ) PV cell in the PV array, and the battery terminal voltage , find the optimal PV array

configuration and the PV array operating point , such

that the PV charger output current is maximized.

3.2 Problem Decomposition We propose a near-optimal solution to the PAR problem using a novel method that consists of a kernel algorithm, an MPTT control algorithm, and an outer loop finding the optimal number of PV groups in the PV array. The kernel algorithm finds the optimal PV array configuration such that all PV cells can work near their MPPs. The kernel algorithm derives the optimal PV array configuration for a given value to maximize the PV array MPP output power. The MPP output

power of the PV array is the maximum achievable value

under a given solar irradiance and temperature distribution on the PV array, and a given PV array configuration. The subsequent MPTT control algorithm aims to find the optimal PV array

operating point taking into account the PV charger

efficiency variation, such that is maximized. We use the

optimal PV array configuration obtained via the kernel algorithm for the subsequent MPTT control algorithm. The outer loop enumerates all the possible values ( ) and finds the optimal one. The outline of this method is given in Algorithm 1. The next section describes the kernel algorithm in detail, which is the key part in Algorithm 1.

Algorithm 1: Near-Optimal Solution of the PAR Problem.

For each possible value ( ):

Run the kernel algorithm to find the optimal PV array

configuration , such that the PV array MPP output power is maximized.

Run the MPTT control algorithm to find the optimal PV array

operating point that maximizes , under the obtained

optimal PV array configuration

The maximal PV charger output current is denoted by .

Find the optimal value that maximizes , and the corresponding

optimal PV array configuration and PV array

operating point .

111

4. THE KERNEL ALGORITHM The maximum solar power that can be drawn from a PV array is the sum of MPP output power of all the PV cells in that array. Under the non-uniformity of solar irradiance and temperature, PV cells in a balanced n-by-m configuration can hardly operate at their MPPs simultaneously. Our reconfiguration technique aims at making all the PV cells operate at, or close to, their MPPs by updating the configuration of the PV array according to current solar irradiance and temperature distributions. In Figure 7, each PV cell is labeled with its MPP output voltage and current. If the

PV array employs the configuration as shown in Figure 7, all PV cells work at their MPPs simultaneously with the PV array output voltage of 3.6 V (1.5+0.9+1.2=3.6 V) and output current of 4.5 A (1.5+1.5+1.5=4.5 A). The goal of our kernel algorithm is to find a configuration for the PV array such that (i) PV cells within the same PV group have very close MPP output voltages and (ii) the sum of MPP output currents of PV cells within the same group is quite similar among all the PV groups.

Sp,1

1 2 3 4 5

8

Sp,6

6

Sp,7

7

Sp,2 Sp,3 Sp,4

9 10 11 12

Sp,9 Sp,10 Sp,11

Ss,5

Ss,8

Group #1

Group #2

Group #3

1.5V

1.0A

1.5V

1.0A

1.5V

1.5A

1.5V

0.5A

1.5V

0.5A

0.9V

1.5A

0.9V

1.5A

0.9V

1.5A

1.2V

1.0A

1.2V

0.5A

1.2V

1.5A

1.2V

1.5A

Figure 7. An illustration of the PV array reconfiguration.

4.1 Simplifying the Problem The kernel algorithm finds the optimal PV array configuration to maximize the PV array MPP output power for the specified number of PV groups in the array. We name the problem simplified PAR (SPAR) problem. We further simplify the SPAR problem assuming ideal PV cells, and name the new problem ideal PV Cell-based SPAR (IC-SPAR) problem. The V-I characteristic of an ideal PV cell is a step function such that

(8)

where

and

denote the MPP output voltage and

current of the i-th PV cell in the PV array, which are calculated

from the solar irradiance and temperature . The ideal PV cell is an effective approximation of the real PV cell. We use

,

, and to denote the MPP output

voltage, current, and power, respectively, of the ideal PV cell

array with a configuration of . These values are calculated as:

(9)

(10)

(11)

Thus the IC-SPAR problem becomes: find the optimal array configuration (corresponding to the optimal

alphabetical partitioning , , , and ) for a given value,

such that the value calculated from (11) is maximized.

4.2 The Pareto-Optimal Substructure We consider a reduced-size PV array consisting of the first PV cells of the original -cell PV array. The reduced-

size L-cell PV array is composed of PV groups. We

denote a possible configuration of the L-cell PV array by .

Finding the optimal -cell PV array configuration is equivalent to

finding the optimal alphabetical partitioning

of

the set = . The configuration is optimal when the

MPP output power

is maximized. We use

and

to denote the MPP output voltage and current of the PV array with

configuration , respectively. We name the new problem the

reconfiguration problem. The more general reconfiguration problem becomes the original IC-SPAR problem

when and . We find the Pareto-optimal substructure property of this reconfiguration problem as follows.

Definition 1 (Pareto superiority): Consider two configurations

and of the reconfiguration problem. Configuration

is Pareto-superior to if

and

, or

and

.

Definition 2 (Pareto-optimal configuration and Pareto-optimal

set): A configuration is a Pareto-optimal configuration of the

reconfiguration problem if no other configuration of the

reconfiguration problem is Pareto superior to . The set

of all Pareto-optimal configurations of the reconfiguration problem is the Pareto-optimal (configuration) set of the problem.

Next we present two theorems. Theorem 1 demonstrates that the optimal configuration of each reconfiguration problem is an element in the Pareto-optimal set of that problem, whereas Theorem 2 provides the Pareto-optimal substructure property. Proofs are omitted due to limited space.

Theorem 1 (Optimal configuration and Pareto-optimal

configurations): The optimal configuration (with the

maximum MPP output power ) of the

reconfiguration problem is an element in the Pareto-optimal set of

the reconfiguration problem.

Theorem 2 (The Pareto-optimal substructure): Suppose that a

configuration , corresponding to an alphabetical partitioning

, is a Pareto-optimal configuration of the

reconfiguration problem, and the last (the -th) PV group

consists of

cells. Then the alphabetical partitioning

(or the corresponding configuration) must also be Pareto-

optimal in the reconfiguration problem.

4.3 The MCHV Function Based on the above-described Pareto-optimal substructure property, one can find the optimal solution of the original IC-SPAR problem by storing the complete Pareto-optimal set of each

reconfiguration problem with and , in a way similar to the conventional dynamic programming. However,

cardinality of the Pareto-optimal set of the reconfiguration problem could be in the order of , which implies that the Pareto-optimal set cardinality could be exponential. Hence, it is

impractical to store the whole Pareto-optimal set of each reconfiguration problem to solve the original IC-SPAR problem.

For effectively solving the IC-SPAR problem, we introduce a new function, named maximal_current_higher_voltage (MCHV)

function for each reconfiguration problem, denoted by

. The MCHV function

derives the maximum

value achieved by any configuration of the

reconfiguration problem satisfying , i.e.,:

112

(12)

If there exists no configuration satisfying for

relatively large values, we have . The domain of

the MCHV function for the reconfiguration problem is

given by

, where

and

values are the estimated lower and upper bounds of the

value for any configuration , respectively. The

and

values are calculated by

(13)

(14)

Finding tighter upper and lower bounds is an interesting problem, but it is outside the scope of the present paper. An illustration of the MCHV function is shown in Figure 8.

The MCHV function is a non-increasing function with a set of points of discontinuity. Each point of discontinuity in the MCHV function corresponds to a Pareto-optimal configuration of the

reconfiguration problem. Point shown in

Figure 8 corresponds to a Pareto-optimal configuration with

and

, since we have

for any configuration of the

reconfiguration problem satisfying . Finally, the

MCHV function of each reconfiguration problem fully represents the Pareto-optimal set of that problem.

, ,

, ,ˆ

IC

MPP L l

pv maxV

V

,, L la MCHV aV f V

,L lMCHVf

,, L lb MCHV bV f V

ˆIC

MPP,L,l

pv, ,minV

( 1)k k

......ˆIC

MPP,L,l

pv, ,minVˆ

IC

MPP,L,l

pv, ,minV

Figure 8. An illustration of the MCHV function.

4.4 Implementation of Kernel Algorithm In the MCHV function for an reconfiguration problem, the total number of points of discontinuity could also be exponential. Hence, we represent the MCHV function in discrete domain. We

define a three-dimensional matrix , where

stores the

value. In the above expression,

,

and is the predefined precision level in the kernel algorithm. When , the array fully

represents the MCHV function , which is however not

practical since the size of is infinite. When is finite,

the Pareto-optimal configurations of the reconfiguration problem can be classified into two categories: observable and unobservable Pareto-optimal configurations. Consider a Pareto-

optimal configuration of the reconfiguration problem

satisfying

.

Then is observable if , and is

unobservable otherwise (i.e., .) An

example of observable Pareto-optimal configuration is the one

corresponding to the point in Figure 8, and an

example of unobservable Pareto-optimal configuration is the one

corresponding to the point The following lemma

and theorem prove that we can find an approximate solution of the IC-SPAR problem by considering only the observable Pareto-optimal configurations in the kernel algorithm implementation.

Lemma 1 (Bound on MPP output power of unobservable Pareto-optimal configurations): For each unobservable Pareto-optimal

configuration of the reconfiguration problem satisfying

, there

exists a corresponding observable Pareto-optimal configuration

with

and

. Besides, the MPP

output power of the unobservable Pareto-optimal

configuration is bounded as follows:

(15)

Theorem 3 (Approximate solution): We use to denote the near-optimal solution (configuration) of the IC-SPAR problem obtained by considering only the observable Pareto-optimal configurations in the kernel algorithm implementation, with

details shown in Algorithm 2. We use to denote the true optimal solution (configuration) of the IC-SPAR problem. Then

the MPP output power of the near-optimal

configuration is bounded as follows:

(16)

where is a function of the predefined parameter and converges to 0 when .

Since the number of observable Pareto-optimal configurations for each reconfiguration problem is bounded by , practical implementation of the kernel algorithm is feasible. Details of the proposed dynamic programming based kernel algorithm to solve the IC-SPAR problem are provided in Algorithm 2. The solution of the IC-SPAR problem serves as the near-optimal solution of the SPAR problem, and the original PAR problem can be further solved using Algorithm 1.

Algorithm 2: The Kernel Algorithm.

Maintain three-dimensional matrices , ,

and . Each has rows, columns and layers.

Initialization:

and

for and .

The rest of entries in all four matrices , ,

and are initialized to be zero.

For from to :

For from to :

Calculate

and values using (13) and (14).

Calculate using

.

For from to :

,

s.t. .

In the above expressions:

,

.

If :

,

s.t. .

.

.

The near-optimal MPP output power of the PV array can be calculated by

.

Trace back the three-dimensional matrices and

to find the near-optimal configuration of the PV array.

113

5. EXPERIMENTAL RESULTS We compare the performances of two PV systems: one is the proposed system with reconfiguration technique, and the other is the baseline system without reconfiguration technique. Both PV systems contain a PV array of 60 PV cells, a charger and a battery bank. The PV array in the proposed system has the reconfiguration structure shown in Figure 5 while the PV array in the baseline system has a fixed 6x10 configuration, where 6 PV cell groups are connected in series and each PV group consists of 10 parallel-connected PV cells. The output power of baseline system is enhanced by the improved MPPT technique [4] and the integration of a bypass diode within each PV cell [6].

(a) (b)

G = 1.00G = 0.50G = 0.25G = 0.15

90 C

10 C

Figure 9. (a) Solar irradiance and (b) temperature

distributions on the PV array.

We simulate the output power levels of the two systems under the solar irradiance and temperature distributions as shown in Figure 9. Although the mounting locations of PV cells in the proposed system are the same as those of PV cells in the baseline system, the PV array in the proposed system shows different configurations achieved by the reconfiguration technique, in

response to different values. Table 1 summarizes the output power improvement of the proposed system compared to the

baseline system with different battery terminal voltage values. The proposed system achieves up to 6X improvement in the output power level with the solar irradiance and temperature

distributions as shown in Figure 9 when 45 V. Table 1 also provides near-optimal configurations obtained from the proposed reconfiguration algorithm.

Table 1. Output power improvement of the proposed PV

system with different values.

( V )

15 30 45

PV array

configuration (9; 3, 12, 4, 4,

14, 4, 4, 12, 3)

(12; 2, 5, 10,

2, 3, 8, 8, 3, 2,

10, 5, 2)

(12; 2, 5, 10,

2, 3, 8, 8, 3, 2,

10, 5, 2)

Power output

improvement 1.99X 2.71X 6.08X

0 5 10 15 20 250

10

20

30

40

Voltage (V)

Po

we

r (W

)

PV System with Reconfiguration

Baseline System

Vbat

= 30 V

Figure 10. The V-P characteristics of the two PV systems.

In Figure 10, we plot the V-P characteristics of PV arrays in the proposed system and the baseline system with the irradiance and

temperature distributions given in Figure 9 when 30 V. The proposed system achieves significantly higher peak output power than that of the baseline system. Since the operating point of the PV array is always set to be its MPP to extract maximum output power out of the PV system, the proposed system outperforms the baseline system in Figure 10. Moreover, the V-P characteristic curve of the proposed system is unimodal even

under irradiance and temperature non-uniformity with the proposed reconfiguration technique, while the V-P characteristic curve of the baseline system has multiple peaks. Therefore, the standard MPTT technique could be incorporated into the proposed system without extra modification. However, the MPPT or MPTT technique must be modified to track a global optimal operating point instead of a local optimal point in the baseline system. A typical modification would be searching the whole operating range of the PV array output voltage and current, which results in significantly higher time overhead compared with standard MPPT or MPTT technique based on the perturb and observe approach.

6. CONCLUSION Non-uniformity of the solar irradiance and temperature on the PV array is a serious obstacle to efficient utilization of the PV system on HEV. This paper presents a dynamic PV array reconfiguration technique with systematic and scalable structural support and a dynamic programming based reconfiguration control algorithm. Experimental results demonstrate that the proposed reconfiguration method results in up to a factor of 6X output power level improvement compared with a baseline PV system.

ACKNOWLEDGEMENTS This work is sponsored by a grant from the U.S. National Science Foundation, the Brain Korea 21 Project, the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST) (No. 2011-0016480), and ICT at Seoul National University.

REFERENCES [1] N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli,

“Optimization of perturb and observe maximum power point

tracking method,” IEEE Trans. on Power Electronics, 2005.

[2] F. Liu, S. Duan, F. Liu, B. Liu, and Y. Kang, “A variable step

size INC MPPT method for PV systems,” IEEE Trans. on

Industrial Electronics, 2008.

[3] Y. Kim, N. Chang, Y. Wang, and M. Pedram, “Maximum power

transfer tracking for a photovoltaic-supercapacitor energy

system,” in ISLPED, 2010.

[4] H. Patel, and V. Agarwal, “Maximum power point tracking

scheme for PV systems operating under partially shaded

conditions,” IEEE Trans. on Industrial Electronics, 2008.

[5] R. Bruendlinger, B. Bletterie, M. Milde, and H. Oldenkamp,

“Maximum power point tracking performance under partially

shaded PV array conditions,” in Proc. 21st EUPVSEC, 2006.

[6] D. Nguyen, and B. Lehman, “An adaptive solar photovoltaic

array using model-based reconfiguration algorithm,” IEEE Trans.

on Industrial Electronics, 2008.

[7] G. Velasco-Quesada, F. Guinjoan-Gispert, R. Pique-Lopez, M.

Roman-Lumbreras, and A. Conesa-Rosa, “Electrical PV array

reconfiguration strategy for energy extraction improvement in

grid-connected PV systems,” IEEE Trans. on Industrial

Electronics, 2009.

[8] M. A. Chaaban, M. Alahmad, J. Neal, J. Shi, C. Berryman, Y.

Cho, S. Lau, H. Li, A. Schwer, Z. Shen, J. Stansbury, and T.

Zhang, “Adaptive photovoltaic system,” in IECON, 2010.

[9] Y. Kim, S. Park, Y. Wang, Q. Xie, N. Chang, M. Poncino, and

M. Pedram, “Balanced reconfiguration of storage banks in a

hybrid electrical energy storage system,” in ICCAD, 2011.

[10] W. Lee, Y. Kim, Y. Wang, N. Chang, M. Pedram, and S. Han,

“Versatile high-fidelity photovoltaic module emulation system,”

in ISLPED, 2011.

[11] Y. Wang, Y. Kim, Q. Xie, N. Chang, and M. Pedram, “Charge

migration efficiency optimization in hybrid electrical energy

storage (HEES) systems,” in ISLPED, 2011.

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